program cauchitburr8
version 13.0
args lnf Xb Xd
tempvar sigma
tempvar mu
quietly {
	gen double `sigma' = exp(`Xd')
	gen double `mu' = `Xb'
	replace `lnf' = log(`sigma') + log(1/sin(_pi*$ML_y1)) - log(`mu'^2 + `sigma'^2 ///
	- 2*`mu'*log(tan((_pi*$ML_y1)/2)) + log(tan((_pi*$ML_y1)/2))^2) 
	}
end
/*
This distribution is from the CDF-quantile family presented in 
Smithson, M. & Shou, Y. (2017). CDF-quantile distributions for modeling 
random variables on the unit interval. 
British Journal of Mathematical and Statistical Psychology, 70(3), 412-438. 
*/